An elasto-visco-plastic model of cell aggregates

Concentrated cell suspensions exhibit different mechanical behavior depending on the mechanical stress or deformation they undergo. They have a mixed rheological nature: cells behave elastically or viscoelastically, they can adhere to each other whereas the carrying fluid is usually Newtonian. We report here on a new elasto-visco-plastic model which is able to describe the mechanical properties of a concentrated cell suspension or aggregate. It is based on the idea that the rearrangement of adhesion bonds during the deformation of the aggregate is related to the existence of a yield stress in the macroscopic constitutive equation. We compare the predictions of this new model with five experimental tests: steady shear rate, oscillatory shearing tests, stress relaxation, elastic recovery after steady prescribed deformation, and uniaxial compression tests. All of the predictions of the model are shown to agree with these experiments.     

The role of stress in the growth of a multicell spheroid

Rather recent experimental results demonstrate the non–negligible role of mechanical stress in the growth of a multicell spheroid. In this paper we discuss a theoretical framework for volumetric growth suitable for modeling the growth of soft tissues exhibiting the properties of a solid. After a proper kinematic decomposition, balance equations for mass, momentum and energy are discussed together with constitutive relationships. The mathematical model is then applied to avascular tumor growth. We show by numerical simulation that, under assumption of spherical symmetry, the mathematical model is able to reproduce the experimental data with a satisfying qualitative agreement.     

Mechanosensitive Channels: Insights from Continuum-Based Simulations

Mechanotransduction plays an important role in regulating cell functions and it is an active topic of research in biophysics. Despite recent advances in experimental and numerical techniques, the intrinsic multiscale nature imposes tremendous challenges for revealing the working mechanisms of mechanosensitive channels. Recently, a continuum-mechanics-based hierarchical modeling and simulation framework has been established and applied to study the mechanical responses and gating behaviors of a prototypical mechanosensitive channel, the mechanosensitive channel of large conductance (MscL) in bacteria Escherichia coli (E. coli), from which several putative gating mechanisms have been tested and new insights are deduced. This article reviews these latest findings using the continuum mechanics framework and suggests possible improvements for future simulation studies. This computationally efficient and versatile continuum-mechanics-based protocol is poised to make contributions to the study of a variety of mechanobiology problems.     

Multi-scale modeling of a wound-healing cell migration assay

A continuum model and a discrete model are developed to capture the population-scale and cell-scale behavior in a wound-healing cell migration assay created from a scrape wound in a confluent cell monolayer. During wound closure, the cell population forms a sustained traveling wave, with close contact between cells behind the wavefront. Cells exhibit contact inhibition of migration and contact-limited proliferation. The continuum model includes the two dominant mechanisms and characteristics of cell migration and proliferation, using a cell diffusivity function that decreases with cell density and a logistic proliferative growth term. The discrete model arises naturally from the continuum model. Individual cells are simulated as continuous-time random walkers with nearest-neighbor transitions, together with a birth/death process. The migration and proliferation parameters are determined by analysing individual mice 3T3 fibroblast cell trajectories obtained during the development of a confluent cell monolayer and in a wound healing assay. The population-scale model successfully predicts the shape and speed of the traveling wave, while the discrete model is also successful in capturing the contact inhibition of migration effects.     

Gradient fluid shear stress regulates migration of osteoclast precursors

Cell migration is highly sensitive to fluid shear stress (FSS) in blood flow or interstitial fluid flow. However, whether the FSS gradient can regulate the migration of cells remains unclear. In this work, we constructed a parallel-plate flow chamber with different FSS gradients and verified the gradient flow field by particle image velocimetry measurements and finite element analyses. We then investigated the effect of FSS magnitudes and gradients on the migration of osteoclast precursor RAW264.7 cells. Results showed that the cells sensed the FSS gradient and migrated toward the low-FSS region. This FSS gradient-induced migration tended to occur in low-FSS magnitudes and high gradients, e.g., the migration angle relative to flow direction was approximately 90° for 0.1 Pa FSS and 0.2 Pa mm^?1 FSS gradient. When chemically inhibiting the calcium signaling pathways of the mechanosensitive cation channel, endoplasmic reticulum, phospholipase C, and extracellular calcium, the cell migration toward the low-FSS region was significantly reduced. This study may provide insights into the mechanism of the recruitment of osteoclast precursors at the site of bone resorption and of mechanical stimulation-induced bone remodeling.     

Integrin organization: linking adhesion ligand nanopatterns with altered cell responses

This paper presents a modelling framework in which the mechanochemical properties of smooth muscle cells may be studied. The activation of smooth muscles is considered in a three-dimensional continuum model which is key to realistically capture the function of hollow organs such as blood vessels. On the basis of a general thermodynamical framework the mechanical and chemical phases are specialized in order to quantify the coupled mechanochemical process. A free-energy function is proposed as the sum of a mechanical energy stored in the passive tissue, a coupling between the mechanical and chemical kinetics and an energy related purely to the chemical kinetics and the calcium ion concentration. For the chemical phase it is shown that the cross-bridge model of Hai and Murphy [1988. Am. J. Physiol. Cell Physiol. 254, C99-C106] is included in the developed evolution law as a special case. In order to show the specific features and the potential of the proposed continuum model a uniaxial extension test of a tissue strip is analysed in detail and the related kinematics and stress-stretch relations are derived. Parameter studies point to coupling phenomena; in particular the tissue response is analysed in terms of the calcium ion level. The model for smooth muscle contraction may significantly contribute to current modelling efforts of smooth muscle tissue responses.     

Residual stress generation and necrosis formation in multi-cell tumour spheroids

We consider how cell proliferation and death generate residual stresses within a multi-cell tumour spheroid (MCTS). Previous work by Jones and co-workers [8] has shown that isotropic growth in a purely elastic MCTS produces growth induced stresses which eventually become unbounded, and hence are physically unrealistic. Since viscoelastic materials show stress relaxation under a fixed deformation we consider the effect of the addition of a small amount of viscosity to the elastic system by examining formation of equilibrium stress profiles within a Maxwell type viscoelastic MCTS. A model of necrosis formation based upon that proposed by Please and co-workers (see [16] [17] [18]) is then presented in which necrosis forms under conditions of adverse mechanical stress rather than in regions of extreme chemical stress as is usually assumed. The influence of rheology on necrosis formation is then investigated, and it is shown that the excessive stress generated in the purely elastic tumour can be relieved either by the addition of some viscosity to the system or by accounting for an inner necrotic interface with an appropriate stress boundary condition.     

Quantifying the contribution of actin networks to the elastic strength of fibroblasts

The structural models created to understand the cytoskeletal mechanics of cells in suspension are described here. Suspended cells can be deformed by well-defined surface stresses in an Optical Stretcher [Guck, J., Ananthakrishnan, R., Mahmood, H., Moon, T.J., Cunningham, C.C., K?s, J., 2001. The optical stretcher: a novel laser tool to micromanipulate cells. Biophys. J. 81(2), 767-784], a two-beam optical trap designed for the contact-free deformation of cells. Suspended cells have a well-defined cytoskeleton, displaying a radially symmetric actin cortical network underlying the cell membrane with no actin stress fibers, and microtubules and intermediate filaments in the interior. Based on experimental data using suspended fibroblasts, we create two structural models: a thick shell actin cortex model that describes cell deformation for a localized stress distribution on these cells and a three-layered model that considers the entire cytoskeleton when a broad stress distribution is applied. Applying the models to data, we obtain a (actin) cortical shear moduli G of approximately 220 Pa for normal fibroblasts and approximately 185 Pa for malignantly transformed fibroblasts. Additionally, modeling the cortex as a transiently crosslinked isotropic actin network, we show that actin and its crosslinkers must be co-localized into a tight shell to achieve these cortical strengths. The similar moduli values and cortical actin and crosslinker densities but different deformabilities of the normal and cancerous cells suggest that a cell's structural strength is not solely determined by cytoskeletal composition but equally importantly by (actin) cytoskeletal architecture via differing cortical thicknesses. We also find that although the interior structural elements (microtubules, nucleus) contribute to the deformed cell's exact shape via their loose coupling to the cortex, it is the outer actin cortical shell (and its thickness) that mainly determines the cell's structural response.     

Thermal expansion of blood vessels in low cryogenic temperatures Part I: A new experimental device

As part of the ongoing effort to study the mechanical behavior of biological material during cryopreservation processes, the current study focuses on thermal expansion of blood vessels at low cryogenic temperatures. The current paper (Part I) describes a new experimental device for thermal expansion measurements of blood vessels in typical conditions of vitrification, which are associated with rapid cooling rates. For validation purposes, the thermal strain of frozen arteries in the absence of cryoprotectants was measured, and found to be about 10% larger than that of polycrystalline water; this observation agrees with literature data. The companion paper (Part II) reports on experimental results of cryoprotectants permeated with VS55, DP6, and 7.05 M DMSO at high cooling rates applicable to vitrification.     

Thermal expansion of blood vessels in low cryogenic temperatures, Part II: Vitrification with VS55, DP6, and 7.05 M DMSO

As part of the ongoing effort to study the mechanical behavior of biological materials in cryopreservation processes, the current study focuses on thermal expansion during vitrification (vitreous in Latin means glassy). A new device is utilized in this study, which has been described in detail in the companion paper (Part I). The current study (Part II) focuses on measurements of vitrified blood vessels permeated with the cryoprotectants VS55, DP6, and DMSO. Data analysis in this study includes polynomial approximation of experimental results in the lower part of the cryogenic temperature range, where the material behaves as solid over a practical time scale. The study further includes a unified thermal expansion analysis throughout the entire cryogenic temperature range by compiling the current results with previously reported data. Finally, analysis of the glass transition temperature, based on thermal strain data is presented.